Spock enters a turbollift at the interior end of the shuttlebay, he arrives directly at the bridge. Those two points are on a perfect diagonal, it's entirely possible there is a 45 degree shaft desgined for much more rapid transit from the bay to the bridge.
Which is something I always wanted to see since being opposite ends of the ship, during an emergency, there would need to be something for much faster travel.
The shuttlebay scene, the engineering sections, the bridge exterior 'looking in' shots, the size and amount of the dilitium reactors all show a ship nearly 500 meters long.
The pod landing on Delta Vega is detailed, whereas the object fired from the ship is smooth and bullet shaped, obviously a first stage re-entry covering for the pod Jim is in, maybe even carrying several pods if need be.
Few if any shots give reason to believe this ship is 400m or lower, and far too many give it at 500+